References
[1]. Asadi, A. R., & Hemadi, R. (2018, November). Understanding Virtual Currencies in Video Games: A Review. In 2018 2nd National and 1st International Digital Games Research Conference: Trends, Technologies, and Applications (DGRC) (pp. 109-117). IEEE.
[2]. Boden, J., Maier, E., & Wilken, R. (2020). The effect of credit card versus mobile payment on convenience and consumers’ willingness to pay. Journal of Retailing and Consumer Services, 52, 101910.
[3]. Shallit, J. (2003). What this country needs is an 18c piece. Mathematical Intelligencer, 25(2), 20-23.
[4]. Lueker, G. S. (1975). Two NP-complete problems in nonnegative integer programming. Princeton University. Department of Electrical Engineering, Princeton University.
[5]. Keller J B. (1976). Inverse problems. Amer Math Monthly, 83: 107–118.
[6]. Cormen, T., Leiserson, C., Rivest, R., & Stein, C. (2009). Introduction to Algorithms. MIT Press. Problem 16-1, p. 446.
[7]. Goodrich, M. T., & Tamassia, R. (2015). Algorithm design and applications (Vol. 363). Hoboken: Wiley.
[8]. Chan, T. M., & He, Q. (2020). On the change-making problem. In Symposium on Simplicity in Algorithms (pp. 38-42). Society for Industrial and Applied Mathematics.
[9]. Wright, J. W. (1975). The change-making problem. Journal of the ACM (JACM), 22(1), 125-128.
[10]. Adamaszek, A., & Adamaszek, M. (2010). Combinatorics of the change-making problem. European Journal of Combinatorics, 31(1), 47-63.
[11]. Owlree — The Change-Making Problem. (n.d.). owlree.blog. https://owlree.blog/posts/change-making-problem.html.
[12]. Pearson, D. (2005). A polynomial-time algorithm for the change-making problem. Operations Research Letters, 33(3), 231-234.
[13]. Cai, X. (2009, August). Canonical coin systems for change-making problems. In 2009 Ninth International Conference on Hybrid Intelligent Systems (Vol. 1, pp. 499-504). IEEE.
Cite this article
Yin,X. (2023). Bilateral optimal denomination problem. Theoretical and Natural Science,5,899-904.
Data availability
The datasets used and/or analyzed during the current study will be available from the authors upon reasonable request.
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References
[1]. Asadi, A. R., & Hemadi, R. (2018, November). Understanding Virtual Currencies in Video Games: A Review. In 2018 2nd National and 1st International Digital Games Research Conference: Trends, Technologies, and Applications (DGRC) (pp. 109-117). IEEE.
[2]. Boden, J., Maier, E., & Wilken, R. (2020). The effect of credit card versus mobile payment on convenience and consumers’ willingness to pay. Journal of Retailing and Consumer Services, 52, 101910.
[3]. Shallit, J. (2003). What this country needs is an 18c piece. Mathematical Intelligencer, 25(2), 20-23.
[4]. Lueker, G. S. (1975). Two NP-complete problems in nonnegative integer programming. Princeton University. Department of Electrical Engineering, Princeton University.
[5]. Keller J B. (1976). Inverse problems. Amer Math Monthly, 83: 107–118.
[6]. Cormen, T., Leiserson, C., Rivest, R., & Stein, C. (2009). Introduction to Algorithms. MIT Press. Problem 16-1, p. 446.
[7]. Goodrich, M. T., & Tamassia, R. (2015). Algorithm design and applications (Vol. 363). Hoboken: Wiley.
[8]. Chan, T. M., & He, Q. (2020). On the change-making problem. In Symposium on Simplicity in Algorithms (pp. 38-42). Society for Industrial and Applied Mathematics.
[9]. Wright, J. W. (1975). The change-making problem. Journal of the ACM (JACM), 22(1), 125-128.
[10]. Adamaszek, A., & Adamaszek, M. (2010). Combinatorics of the change-making problem. European Journal of Combinatorics, 31(1), 47-63.
[11]. Owlree — The Change-Making Problem. (n.d.). owlree.blog. https://owlree.blog/posts/change-making-problem.html.
[12]. Pearson, D. (2005). A polynomial-time algorithm for the change-making problem. Operations Research Letters, 33(3), 231-234.
[13]. Cai, X. (2009, August). Canonical coin systems for change-making problems. In 2009 Ninth International Conference on Hybrid Intelligent Systems (Vol. 1, pp. 499-504). IEEE.